Many existing gaming machines, such as traditional slot machines, include bonus rounds. Typically, a bonus round begins when the player reaches a bonus triggering event in the primary game of the gaming device. In slot machines with reels, the triggering event usually occurs when the player reaches a predetermined combination of symbols on the reels. Usually, the bonus scheme provides the player with an opportunity to gain a bonus value before the bonus round terminates. Some of these existing bonus schemes involve players making inputs and receiving values associated with the outcomes of the inputs. To increase player enjoyment and excitement, it is desirable to provide players with new gaming device bonus schemes.